pub fn new_birthday_probability(n: u32) -> f64 {
    const DAYS : u32 = 365; 
    
    let mut prob_all_different_days = 1.0;
    for k in 0..n {
        prob_all_different_days *= (DAYS - k) as f64 / DAYS as f64;
    }
    
    1.0 - prob_all_different_days
}
